There is a concept called a statutory instrument in which the process is optimized by allowing changes to be made to law either by "laying them before" Parliament, in which case only approval or rejection is possible, not amendment. Annulling new regulations in this manner is extremely rare however. Or in some cases it's allowed for the responsible Minister or committee of MPs to make the changes directly, which in practice means they sign off on changes proposed by the civil service. This is usually only the case for very minor changes like updating thresholds, shutting down roads for construction work etc.

Despite the inability of the civil service to directly change the law, the UK is not suffering from a deficit of regulations. So there's no reason in principle it should harm productivity, unless you mean, productivity of the government itself.